Which of the following numbers is a factor of 130? ${3,4,5,7,8}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $130$ by each of our answer choices. $130 \div 3 = 43\text{ R }1$ $130 \div 4 = 32\text{ R }2$ $130 \div 5 = 26$ $130 \div 7 = 18\text{ R }4$ $130 \div 8 = 16\text{ R }2$ The only answer choice that divides into $130$ with no remainder is $5$ $ 26$ $5$ $130$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $5$ are contained within the prime factors of $130$ $130 = 2\times5\times13 5 = 5$ Therefore the only factor of $130$ out of our choices is $5$. We can say that $130$ is divisible by $5$.